Let f: (−π / 2, π / 2) → R be given by f (t) = tan^−1(t). a) What is Taylor's polynomial P1 (t) of order 1 f if t = 0? What is the remainder E1 (t) in Taylor's formula f (t) = P1 (t) + E1 (t)? b)Use Taylor's residual formula to give an estimate of π / 4 = tan ^ −1 (1) (without to use the π button on the calculator): Show that the residual term E1 (1) is in between −1 and 0 and that π / 4 is equal to P1 (1) - 1/4 = 3/4 with an error less than 1/4.

Let f: (−π / 2, π / 2) → R be given by f (t) = tan^−1(t). a) What is Taylor's polynomial P1 (t) of order 1 f if t = 0? What is the remainder E1 (t) in Taylor's formula f (t) = P1 (t) + E1 (t)? b)Use Taylor's residual formula to give an estimate of π / 4 = tan ^ −1 (1) (without to use the π button on the calculator): Show that the residual term E1 (1) is in between −1 and 0 and that π / 4 is equal to P1 (1) - 1/4 = 3/4 with an error less than 1/4.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 3E

See similar textbooks